Single Tooth Bending Fatigue Tests Research Articles

Numerical Study of the Impact of Shot Peening on the Tooth Root Fatigue Performances of Gears Using Critical Plane Fatigue Criteria

Gears are one of the the most widespread mechanical components and their design is supported by standard calculation methods. Among all the possible failure modes of gears, tooth root bending is the most critical and could lead to catastrophic failures. In this regard, different surface treatments could be exploited to improve the gear strength. Among them, shot peening is the most common. The aim of this study is to evaluate the effectiveness of shot peening on improving the tooth root bending resistance. This is achieved by exploiting the Finite Element Method (FEM) in combination with advanced multiaxial fatigue criterion based on the critical plane concept. A standard Single Tooth Bending Fatigue test was reproduced numerically via FEM. Beside the wrought gears, shot peened ones were also simulated. The state of stress induced by the shot peening was obtained numerically by simulating the surface treatment itself with non-linear dynamic analyses. The results have shown quantitatively how the residual stresses promote an improvement in the resistance and how the local hardening could lead to different early paths of nucleation and propagation of cracks on the tooth fillet.

Gear Tooth Root Bending Strength Estimation under the Assumption of Fatigue Limit Existence

Being able to properly predict gear failure is a key aspect to achieve a reliable light-weight gearbox. Among the several gear failures, tooth root bending fatigue is considered as the most dangerous one because it implies the stoppage of the whole gearbox. In order to characterize a gear for this phenomena, Single Tooth Bending Fatigue (STBF) tests are the most performed ones. However, as in STBF test THERE IS no sliding/rolling contact and as the specimens are teeth rather than gears, some differences occur between the test conditions and those of the real case. This paper deals with the statistical ones that is the estimation of the gear SN curve starting from the teeth one. The teeth SN curve has been estimated by means of a statistical model developed considering Murakami’s idea of nonpropagating crack. Then, a methodology based on statistic of extreme is adopted for the purpose of estimating the gear SN curve.

Computational model for bending fatigue prediction of surface hardened spur gears based on the multilayer method

A computational model for predicting both the location and the required number of cycles for bending fatigue failure in surface hardened spur gears is proposed. Linear elastic stresses and strains in a single tooth bending fatigue test are corrected for elastic–plastic material behavior. The tooth root region of spur gear is divided into layers. Fatigue properties are assigned to each layer via the hardness method. Based on the multiaxial fatigue criteria, fatigue failure location and corresponding fatigue lives are estimated. Predicted fatigue lives, failure locations, and transition from surface to subsurface fatigue failure show good agreement with the experimental results.

Effect of layer orientation on the single tooth bending fatigue strength of polymer gears manufactured by selective laser sintering

This study investigates the influence of tooth layer orientation on the bending fatigue behaviour of Nylon 12 spur gears manufactured by a selective laser sintering process in an ‘on-edge’ configuration. The test gears were submitted to single tooth bending fatigue tests, and the thermal response of gears was recorded using Infrared thermography. The surface morphology of failed teeth was examined using microscopy. The effect of tooth layer orientation on the fatigue strength of selective laser sintering gears was evaluated by testing each tooth configuration. The tooth configurations with the highest and lowest strength were 40° and 160°, respectively. The performance of selective laser sintering gears was compared with that of injection moulded Nylon 66 gears. The injection moulded, selective laser sintering 40°, and selective laser sintering 160° gear teeth were tested at multiple loads to investigate the high cycle fatigue and low cycle fatigue behaviour. The bending fatigue life was highest for the injection moulded gears in both low cycle fatigue and high cycle fatigue regimes. The surface temperature was higher in selective laser sintering gears, with 160° configuration exhibiting the highest temperature. The difference between the temperatures of selective laser sintering 40° configuration and injection moulded gear magnified as the applied load increased. Consequently, the strength of the selective laser sintering 40° configuration with respect to injection moulded gear deteriorated in the low cycle fatigue region. Fractography indicated that crack propagation in selective laser sintering 40° and selective laser sintering 160° configurations were cross-laminar and inter-laminar, respectively. In the cross-laminar mode of propagation, the crack propagation was impeded by the layer structure. However, the crack propagation was expedited in the inter-laminar mode, as the crack path was along the interlayer region, which presents a path of least resistance.

Gear root bending strength: statistical treatment of Single Tooth Bending Fatigue tests results

Gear tooth failure due to tooth root bending fatigue is one of the most dangerous failure modes in gears. Therefore, the precise definition of gear bending fatigue strength is a key aspect. Furthermore, in order to calculate the service life of a gear component, an accurate estimation of the S‑N curve is required. This curve must properly account for the slope of the fatigue strength region, the slope of the region ahead the fatigue knee, as well as the position of the knee itself. Hence, in order obtain a curve at different reliability levels, a proper estimation of the dispersion associated with the experimental points is required. Usually, Single Tooth Bending Fatigue (STBF) tests are used to investigate the gear load carrying capacity with respect to the bending failure mode. Then, starting from the gear specimen test data, the S‑N curve that has to be used in the rating method has to be determined. Maximum Likelihood Estimation (MLE), a statistical tool capable of considering also interrupted tests (e.g. runouts) has been used to estimate, in the most reliable way, the S‑N curve from experimental points. Furthermore, if the STBF test is performed in a symmetrical configuration, i.e. two teeth loaded at the same time, also the survival of one of the two teeth represents an information that can be taken into account thanks to MLE.Moreover, additional effects must be considered to obtain the S‑N curve of a real component starting from STBF tests. In reality, the load history and the statistical behaviour are different, since in a meshing gear the strength is determined by its weakest tooth, while in a STBF test the failing tooth is predetermined. The latter effect is considered by means of the statistic of extremes, which enables the estimation of the strength of the weakest tooth and therefore of the gear. This paper describes in detail the proposed calculation method and explains its application to determine the S‑N curve in practical cases.

Comparison of the bending fatigue performances of selective laser sintered and injection moulded nylon spur gears

This study compares the bending fatigue performance of a selective laser sintered Nylon 12 spur gear with an injection moulded Nylon 66 gear. Test gears were subjected to load-controlled, single tooth bending fatigue tests in a custom-built test setup. Cyclic pulsating loads were applied on the test gear using a steel driver gear. The bending fatigue life of selective laser sintered gears was superior compared to the injection moulded gears. In the high cycle fatigue region, the difference between the fatigue life of selective laser sintered and injection moulded gears was higher, whereas it was lower in the low cycle fatigue region. The variation in the fatigue strength of the selective laser sintered gears was due to the different thermal behaviour at low cycle fatigue and high cycle fatigue regimes. The lower surface temperature caused the higher fatigue strength of the selective laser sintered gears in the high cycle fatigue regime. On the contrary, the selective laser sintered gears’ surface temperature was higher than injection moulded gear in the low cycle fatigue regime, which reduced fatigue strength. The crack path was tortuous in selective laser sintered gears and smoother in injection moulded gears. In selective laser sintered gears, the layered structure of the part aided in impeding the propagation of crack.

An analysis of the effect of pressure angle change on bending fatigue performance in asymmetrical spur gears

In this study, the fatigue performances of symmetrical and asymmetrical spur gears were analyzed by performing single tooth bending fatigue tests. The gears tested were determined to be symmetrical spur gears with a 20°/20° pressure angle, asymmetrical spur gears with a 20°/22° pressure angle, and asymmetrical spur gears with a 20°/25° pressure angle. These gears were made of AISI 4140 material. Single tooth bending fatigue tests were performed under variable loads. Considering the tests performed at the same torque values in asymmetrical spur gears with a 20°/22° pressure angle compared to symmetrical spur gears with a 20°/20° pressure angle, a statistically significant increase in performance was achieved at close to 90%. While gears with 20°/20° and 20°/22° pressure angles break at the tooth root, tooth flank fracture was observed in relatively high numbers of cycles in asymmetric spur gears with a 20°/25° pressure angle. It was observed that the formation of tooth flank damage negatively affected the fatigue performance.

Gear Root Bending Strength: A New Multiaxial Approach to Translate the Results of Single Tooth Bending Fatigue Tests to Meshing Gears

Developing accurate design data to enable the effective use of new materials is undoubtedly an essential goal in the gear industry. To speed up this process, Single Tooth Bending Fatigue (STBF) tests can be conducted. However, STBF tests tend to overestimate the material properties with respect to tests conducted on Running Gears (RG). Therefore, it is common practice to use a constant correction factor fkorr, of value 0.9 to exploit STBF results to design actual gears, e.g., through ISO 6336. In this paper, the assumption that this coefficient can be considered independent from the gear material, geometry, and loading condition was questioned, and through the combination of numerical simulations with a multiaxial fatigue criterion, a method for the calculation of fkorr was proposed. The implementation of this method using different gear geometries and material properties shows that fkorr varies with the gears geometrical characteristics, the material fatigue strength, and the load ratio (R) set in STBF tests. In particular, by applying the Findley criterion, it was found that, for the same gear geometry, fkorr depends on the material as well. Specifically, fkorr increases with the ratio between the bending and torsional fatigue limits. Moreover, through this method it was shown that the characteristics related to the material and the geometry have a relevant effect in determining the critical point (at the tooth root) where the fracture nucleates.

Gear Root Bending Strength: A Comparison Between Single Tooth Bending Fatigue Tests and Meshing Gears

Abstract Gear tooth breakage due to bending fatigue is one of the most dangerous failure modes of gears. Therefore, the precise definition of tooth bending strength is of utmost importance in gear design. Single tooth bending fatigue (STBF) tests are usually used to study this failure mode since they allow to test gears, realized and finished with the actual industrial processes. Nevertheless, STBF tests do not reproduce exactly the loading conditions of meshing gears. The load is applied in a predetermined position, while in meshing gears, it moves along the active flank; all the teeth can be tested and have the same importance, while the actual strength of a meshing gear, practically, is strongly influenced by the strength of the weakest tooth of the gear. These differences have to be (and obviously are) taken into account when using the results of STBF tests to design gear sets. The aim of this article is to investigate in detail the first aspect, i.e. the role of the differences between two tooth root stress histories. In particular, this article presents a methodology based on high-cycle multi-axial fatigue criteria to translate STBF test data to the real working condition; residual stresses are also taken into account.

Effect of friction on nominal stress results in a single tooth bending fatigue test

One of the main reasons for gear failure is bending fatigue, which occurs due to cyclic stresses at the tooth root region. Bending fatigue can cause crack initiation which, in turn, may propagate and result in catastrophic tooth breakage. Single tooth bending fatigue tests are frequently employed to generate statistically significant fatigue data at relatively low price. Hence, they are often employed as screening tests for bending fatigue behaviour of actual running gear pair. Since relatively small alteration of nominal tooth root stress values can produce significant change in bending fatigue lives, it is important to adequately consider the effect of friction and test fixture deformation when conducting single tooth bending fatigue tests. In this paper, numerical investigation of tooth flank friction effect on spur gear load capacity during single tooth bending fatigue test is carried out. Two different test fixtures are considered. Linear elastic finite element analysis is carried out to obtain nominal tooth root stresses. The results show that friction at gear tooth flank as well as fixture deformation can affect nominal tooth root stress results.

Experimental Study on Fatigue Fracture Damage of Symmetric Spur Gear Tooth

There are many studies on the involute profile symmetric gears in the literature. In many studies done, the critic tooth root stress was emphasized. Studies have been carried out on the calculations of tooth root stress and these studies have been tried to be verified by using the finite element method. Although there are different approaches to calculate the tooth root stress, the most widely used equations are those expressed in ISO and AGMA standards.The studies in the literature have mostly been carried out on the gears that have trochoid curve in the tooth root. In parallel with these studies, experimental studies were done to determine the fatigue life performance of these gears.In this work, involute gears tooth root was manufactured using the circular fillet method which have better tooth root stress than trochoid according to static analyses in literature. Fatigue damage on symmetric gear tooth under cyclic loading and effect of material hardness on fatigue life of gear tooth were investigated.Fatigue tests were performed with specially designed single-tooth bending fatigue test (STBFT) apparatus. The results obtained from fatigue tests at low cycles and high cycles were evaluated comparatively.

密度の異なるNi-Moプレアロイ合金焼結浸炭焼入れ歯車の曲げ疲労強度と空孔を考慮したFEMによる歯元曲げ応力解析

Single tooth bending fatigue tests were first carried out using Ni-Mo pre-alloyed sintered steel (46F4H) spur gears with different densities in the range of 7.30~7.54 Mg/m3. The sintered gears specimens were machined from sintered steel packs made from the single-press single-sinter route and some were surface-rolled using CNC form rolling machine. All test gears were case-carburized. The experimental results showed that the surface-rolled sintered gears with a density of 7.40 Mg/m3 or more had sufficiently high bending fatigue strength to replace gears made of typical Cr-Mo case-carburized wrought steel. Then, the stress analysis in the root fillet area of gear teeth was performed using a FEM simulation model considering a void distribution. The peak value of the maximum principal stress in the surface near the most critical stressed point was increased with the increase of porosity for un-surface rolled gears and was decreased as the amount of surface fully densified depth was increased. These simulation results can explain well the experimental results and show the appropriate material initial density and the surface densification level.

Ni–Mo 系低合金鋼粉を適用した焼結転造浸炭歯車の特性

Finish gear rolling experiments, single tooth bending fatigue tests and gear running tests were carried out using P/M gears made of Ni–Mo pre-alloyed steel powder. A high precision CNC form rolling machine of two-roller dies transverse type was employed. The entire gear tooth flank was successfully densified from the tip to the root fillet by surface rolling. The durability test results show that the test case-carburized P/M gears with a density of 7.5 g/cm3 can achieve bending and surface fatigue strengths of 1.0 GPa and 2.0 GPa, respectively, which completely match with those of case-carburized SCM415 (0.15C–1.0Cr–0.2Mo–0.7Mn) wrought steel gears and those load bearing capacities tend to increase by surface rolling. The compressive residual stress near the gear flank surface is the level of 800 MPa, which is almost equivalent to that of wrought steel gear. The representative damages of P/M gears in gear running tests are pitting, which is the case with the wrought steel gear.

Bending Durability and Impact Strength of Gear Tooth of 1.5Cr-0.2Mo Sintered Alloy Steel Gears for Automotive Transmission

Single tooth bending fatigue tests were carried out using spur gears of 1.5Cr-0.2Mo sintered steel having a density of 7.55 g/cm3 and the effects of surface rolled or shot peening (WPC) on bending fatigue strength were examined. P/M gears were case-carburized. The bending fatigue durability of this P/M gears not surface densified is equal to that of case-carburized wrought alloyed steel gears of SCM415. The bending fatigue limit of the P/M gear was much improved by WPC. The impact strength of P/M gear tooth was investigated using an impact testing machine for gears. The mean value of peak impact damage torque of the surface rolled P/M gears almost matches that of wrought steel gears of SCM415. Both test results indicate the feasibility of this high density Cr-Mo P/M gears to replace case-carburized wrought steel gears made of typical Cr-Mo alloyed steel.

Development of High Precision and Strength Sintered Ferrous Alloy Gear by Rolling -3rd Report-

Surface finish rolling experiments were carried out using P/M spur gears of 0.6Mo-0.2Mn pre-alloyed sintered steel and of 0.8Mo-0.2Mn partially alloyed sintered steel with the density of 7.10 Mg/m3. A CNC form rolling machine of axis intersection type was employed, and a modified screw-shaped rolling tool was prepared: the modified concave tooth profile optimized by numerical tooth profile analysis for simultaneous rolling of tooth and fillet surface. Then, porosity distributions in the surface layer of rolled gear teeth were determined and the effects of the amount of tool radial feed R0 on the selective surface densification behaviors were evaluated. Besides, single tooth bending fatigue test was conducted. Gears with good tooth profiles were obtained by using the modified tools. As a result, the porosities in both the tooth flank and the fillet at the root were reduced to the target level at R0=600 μm in simultaneous rolling process. Furthermore, the single tooth bending fatigue durability was much improved to about 60 % of the case hardened wrought steel gears of SCM415.

鉄系焼結合金歯車の転造による高精度化・高強度化―第２報―修整歯形工具による鉄系焼結合金歯車の各種転造特性

Surface finish rolling experiments were carried out using P/M spur gears of 0.6Mo-0.2Mn pre-alloyed sintered steel and of 0.8Mo-0.2Mn partially alloyed sintered steel with the density of 7.10 Mg/m3. A CNC form rolling machine of axis intersection type was employed. Three kinds of screw-shaped rolling tools were prepared: one was an unmodified tool and the others were the modified tools for simultaneous rolling of tooth and fillet surface having concave tooth profiles optimized by numerical tooth profile analysis. Porosity distributions in the surface layer of rolled gear teeth were determined and the effects of the amount of tool radial feed R0 on the selective surface densification behaviors were evaluated. Single tooth bending fatigue test was conducted. Gears with good tooth profiles were obtained by using the modified tools. The porosities in both the tooth flank and the fillet at the root were reduced to the target level at R0=600 μm in simultaneous rolling process. The single tooth bending fatigue durability was much improved to the same level as that of the wrought steel gears of SCM415.

Three point load application in single tooth bending fatigue test for evaluation of gear blank manufacturing methods

This study deals with the applicability of a single tooth bending fatigue test in the evaluation of gear blank manufacturing methods using three point bending loading. The “single tooth bending test” is an effective and rapid way of determination of the performances of gears instead of expensive and time-consuming life tests. Bending tests were applied to two groups of gears cut by hobbing and gear shaving from gear blanks. The first group of gear blanks was obtained by CNC-lathe machining from round bars and the second group of blanks was produced by closed-die upsetting. Both of the gear groups were additionally tested after case hardening by carburizing. It was shown that the three point bending test can easily be adapted and applied as an effective and rapid way of comparing the performances of such gears.

Comparative bending fatigue strength of precision forged spur gears

To determine the bending fatigue strength of precision forged spur gears and to compare the results with those obtained from conventional cut gears, single tooth bending fatigue tests were carried out on both through-hardened and induction-hardened gear teeth. The gears were produced from rolled bar cut blanks, disc forged blanks or precision forged teeth blanks. For this purpose, a special test fixture was designed and built for an Amsler high-frequency vibrophore fatigue testing machine. The results show that the endurance limit of precision forged gears is significantly higher than those obtained from cut gears. The bending fatigue strength of forged gears was some 12.5 per cent higher than the cut teeth in a through-hardened condition and 8.4 per cent higher for the induction-hardened teeth. The effect of surface roughness at the tooth root area on the bending fatigue strength of the forged gears is also shown.